Apochromatic pancharatnam berry phase (PBP) liquid crystal structures for head-mounted displays

ABSTRACT

A Pancharatnam Berry Phase (PBP) liquid crystal structure for adjusting or focusing light of a plurality of color channels emitted by a display of a head-mounted display (HMD) comprises a plurality of PBP active elements. Each PBP active element of the structure is configured to act as a half waveplate for light of a corresponding color channel, such that light of the corresponding color channel is adjusted by a predetermined amount. In addition, each PBP active element acts as a one waveplate for light of the remaining color channels, such that light of the remaining color channels passes through the PBP active element substantially unaffected. As such, the PBP structure is able to adjust incident light of the plurality of color channels uniformly in an apochromatic fashion.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/798,178, filed Oct. 30, 2017, which claims the benefit of U.S.Provisional Application No. 62/415,444, filed Oct. 31, 2016, each ofwhich is incorporated by reference in its entirety.

BACKGROUND

The present disclosure generally relates to design of opticalassemblies, and specifically relates to chromatic error correction ofPancharatnam Berry Phase (PBP) liquid crystal structures for opticalassemblies that may be used in virtual reality (VR), augmented reality(VR), and mixed reality (MR) systems.

PBP liquid crystal components can be used as an integral part of anoptical assembly in a head-mounted display (HMD) that may be part of,e.g., a VR system, an AR system, a MR system, or some combinationthereof. The PBP liquid crystal components can be implemented as PBPliquid crystal gratings and/or PBP liquid crystal lenses. However, bothtypes of PBP components have strong wavelength dependencies on opticalperformance, wherein the diffraction angle or the focus distance of thePBP component varies based upon the wavelength of light. This reducesimage quality in imaging systems that employ an optical assembly withPBP liquid crystal components and a light source that emits light ofmultiple wavelengths or color channels.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a diagram of a head-mounted display (HMD), in accordance withan embodiment.

FIG. 1B is a cross section of a front rigid body of the HMD in FIG. 1A,in accordance with an embodiment.

FIG. 1C shows a diagram of an HMD implemented as a near eye display, inaccordance with an embodiment.

FIG. 1D shows a cross-section view of the HMD implemented as a near eyedisplay.

FIG. 2A illustrates an example of a PBP liquid crystal (LC) lens, inaccordance with some embodiments.

FIG. 2B illustrates an example of liquid crystal orientations in the PBPLC lens of FIG. 2A, in accordance with some embodiments.

FIG. 2C illustrates a section of liquid crystal orientations taken alonga y axis in the PBP LC lens of FIG. 2A, in accordance with someembodiments.

FIG. 3A illustrates an example of a PBP LC grating, in accordance withsome embodiments.

FIG. 3B illustrates an example of liquid crystal orientations in the PBPLC grating of FIG. 3A, in accordance with some embodiments.

FIG. 3C illustrates a section of liquid crystal orientations taken alonga y axis in the PBP LC grating of FIG. 3A, in accordance with someembodiments.

FIG. 4A illustrates color problems that may be present in PBP LCgrating, in accordance with some embodiments.

FIG. 4B illustrates color problems that may be present in PBP LC lens,in accordance with some embodiments.

FIG. 5A illustrates an apochromatic PBP LC grating structure, inaccordance with some embodiments.

FIG. 5B illustrates an apochromatic PBP LC lens structure, in accordancewith some embodiments.

FIG. 6 illustrates another diagram of an apochromatic PBP LC gratingstructure, in accordance with some embodiments.

FIG. 7 illustrates another diagram of an apochromatic PBP LC lensstructure, in accordance with some embodiments.

FIG. 8 is a block diagram of one embodiment of a HMD system in which aconsole operates.

The figures depict embodiments of the present disclosure for purposes ofillustration only. One skilled in the art will readily recognize fromthe following description that alternative embodiments of the structuresand methods illustrated herein may be employed without departing fromthe principles, or benefits touted, of the disclosure described herein.

SUMMARY

A PBP structure is configured to adjust or focus light as part of anoptical assembly in an HMD. The PBP structure comprises one or more PBPplates, one or more PBP active elements, or some combination thereof.Each PBP plate or active element may be a PBP LC grating or a PBP LClens, and corresponds to a wavelength range associated with a particularcolor channel of a set of color channels.

The PBP plates of the PBP structure may comprise at least a first PBPplate and a second PBP plate. The first PBP plate is configured to actas half waveplate for light of a first wavelength range corresponding toa first color channel of a set of color channels, such that light of thefirst wavelength range is adjusted by a first amount, and to act as aone waveplate for at least light of a second wavelength rangecorresponding to a second color channel of the set of color channels,such that light of the second wavelength range is able to pass throughthe first PBP plate without substantially changing direction. The secondPBP plate is configured to act as a half waveplate for light of thesecond wavelength range, such that light of the second wavelength rangeis adjusted by the first amount, and to act as a one waveplate for aleast light of the first wavelength range, such that light of the firstwavelength range is able to pass through the second PBP plate withoutsubstantially changing direction.

In some embodiments, the PBP structure comprises a PBP platecorresponding to each color channel of the set of color channel. EachPBP plate is configured to act as a half waveplate for its respectivecolor channel such that light of the respective color channel isadjusted by the PBP plate by a set amount. In addition, each PBP plateacts as a one waveplate for the remaining color channels of the set ofcolor channels. As such, light from each color channel passing throughthe PBP structure is adjusted by the same amount (e.g., by itscorresponding PBP plate, while passing through the remaining PBP platessubstantially unadjusted).

DETAILED DESCRIPTION

Configuration Overview

One or more embodiments disclosed herein relate to the apochromaticdesign of a (Pancharatnam Berry Phase) PBP structure comprising aplurality of PBP plates. A PBP plate may be made using active liquidcrystal or a liquid crystal polymer with photoalignment technology. PBPplates can achieve multiple or varying focal lengths when designed as alens, or multiple steering angles when designed as a steering plate(also referred to as a grating). In some embodiments, the PBP plate maybe used for static or active operation of a display device.

In some embodiments, a series of PBP plates each associated with adifferent color channel are coupled together to form a PBP structure,such as an apochromatic grating structure or an apochromatic lensstructure. The grating structure is composed of a series of PBP liquidcrystal gratings that are each configured to operate as a half waveplatefor a respective color channel, while operating as a one waveplate (nochange) for the other color channels. Each of the PBP LC gratings isconfigured such that light within their respective color channel isdiffracted to a common angle.

The lens structure is composed of a series of PBP liquid crystal lensesthat are each configured to operate as a half waveplate for a respectivecolor channel, and operate as a one waveplate for the remaining colorchannels. Each of the PBP LC lenses is configured such that light withintheir respective color channel is focused to a common point. The colorcorrected structures may be used in, e.g., an optical element in ahead-mounted display. This is useful to deal with vergence—accommodationconflict in artificial reality environments.

Embodiments of the invention may include or be implemented inconjunction with an artificial reality system. Artificial reality is aform of reality that has been adjusted in some manner beforepresentation to a user, which may include, e.g., a virtual reality (VR),an augmented reality (AR), a mixed reality (MR), a hybrid reality, orsome combination and/or derivatives thereof. Artificial reality contentmay include completely generated content or generated content combinedwith captured (e.g., real-world) content. The artificial reality contentmay include video, audio, haptic feedback, or some combination thereof,and any of which may be presented in a single channel or in multiplechannels (such as stereo video that produces a three-dimensional effectto the viewer). Additionally, in some embodiments, artificial realitymay also be associated with applications, products, accessories,services, or some combination thereof, that are used to, e.g., createcontent in an artificial reality and/or are otherwise used in (e.g.,perform activities in) an artificial reality. The artificial realitysystem that provides the artificial reality content may be implementedon various platforms, including a head-mounted display (HMD) connectedto a host computer system, a standalone HMD, a mobile device orcomputing system, or any other hardware platform capable of providingartificial reality content to one or more viewers.

Head Mounted Display (HMD)

FIG. 1A is a diagram of a head-mounted display (HMD), in accordance withan embodiment. The HMD may be used as part of an artificial realitysystem. As illustrated in FIG. 1A, the HMD 100 includes a front rigidbody 105 and a band 110. The front rigid body 105 is configured to besituated in front of a user's eyes, and the band 110 is configured to bestretched and to secure the front rigid body 105 on the user's head.

In some embodiments, the front rigid body 105 comprises an apparatus onwhich an image is presented to a user. In the embodiment shown in FIG.1A, the front rigid body 105 includes a front side 120A, a top side120B, a bottom side 120C, a right side 120D, and a left side 120E. Theelectronic display is placed near the front rigid body 105. Theremaining sides (e.g., the top side 120B, bottom side 120C, right side120D, and left side 120E) ensure enough distance between the electronicdisplay and eyes of the user for proper presentation of the image. Insome embodiments, the sides 120 of the front rigid body 105 are opaque,such that a user wearing the HMD 100 cannot see outside of the HMD 100.In another embodiment, one or more of the sides 120 may be transparent.

In some embodiments, the front rigid body 105 further includes locators125, an IMU 130, and position sensors 140 for tracking a movement of theHMD 100. The IMU 130 generates, based on motions detected by theposition sensors 140, IMU data which can be analyzed to determine theposition of the HMD 100. The locators 125 on various parts of the HMD100 are traced by the imaging device at which slow calibration data isgenerated for the VR console 110 to identify the position of the HMD100.

In some embodiments, the IMU 130 is located on the front rigid body 105for generating the IMU data responsive to the motion of the HMD 100detected through the position sensors 140. In one aspect, the IMU 130 isplaced on the front side 120A of the front rigid body 105.Alternatively, the IMU 130 is located on any surface of the 120A of thefront rigid body 105. In the embodiment illustrated in FIG. 1A, the IMU130 includes the position sensors 140. In other embodiments, thepositions sensors 125 may not be included in the IMU 130, and may beplaced on any side 120 of the HMD 100.

The locators 125 are located in fixed positions on the front rigid body105 relative to one another and relative to a reference point 145. Inthe example of FIG. 1A, the reference point 145 is located at the centerof the IMU 130. Locators 125, or portions of the locators 125, arelocated on a front side 120A, a top side 120B, a bottom side 120C, aright side 120D, and a left side 120E of the front rigid body 105 in theexample of FIG. 1A.

FIG. 1B is a cross section of the front rigid body 105 of the embodimentof the HMD 100 shown in FIG. 1A. As shown in FIG. 1B, the front rigidbody 105 includes an electronic display 155 placed near the front side120A of the front rigid body 105 facing an eye-box 165, and transmitslight toward the optical block 160. The eye-box 165 is the location ofthe front rigid body 105 where a user's eye 170 is positioned. Hence,light generated from the electronic display 155 propagates to the exitpupil 165 through the optical block 160, for example.

For purposes of illustration, FIG. 1B shows a cross section 150associated with a single eye 170, but another optical block 160,separate from the optical block 160, provides altered image light toanother eye of the user. Additionally, the HMD 100 may include an eyetracking system (not shown). The eye tracking system may include, e.g.,one or more sources that illuminate one or both eyes of the user, andone or more cameras that captures images of one or both eyes of theuser.

The electronic display 155 displays images to the user. In variousembodiments, the electronic display 155 may comprise a single electronicdisplay or multiple electronic displays (e.g., a display for each eye ofa user). Examples of the electronic display 155 include: a liquidcrystal display (LCD), an organic light emitting diode (OLED) display,an inorganic light emitting diode (ILED) display, an active-matrixorganic light-emitting diode (AMOLED) display, a transparent organiclight emitting diode (TOLED) display, some other display, a projector,or some combination thereof.

The optical block 160 is a component that alters light received from theelectronic display 155 and directs the altered light to the exit pupil165. The optics blocks 160 may include a beam steering plate, ageometric phase lens, or some combination thereof. Both the beamsteering plate and the geometric phase lens may correspond to a PBPstructure having a stack of PBP plates, and are described in greaterdetail below. Together, these components of the optical block 160 directthe image light to the exit pupil 165 for presentation to the user. Insome embodiments, the image light directed to the user may be magnified,and in some embodiments, also corrected for one or more additionaloptical errors (e.g., spherical aberration, coma, astigmatism, fieldcurvature, distortion are third order aberrations, etc.) through theoptical block 160.

In some embodiments, where the HMD 100 is part of an AR or MRapplication, the optical block 160 may further receive and alter lightfrom a local area surrounding the HMD 100. For example, light within theenvironment (hereinafter referred to as “external light”) may enter theHMD 100 (e.g., through the front side 120A) to be received by theoptical block 160. In some embodiments, the external light passesthrough the electronic display 155 before being received by the opticalblock 160. In some embodiments, one or more correction lenses (notshown) or other optical elements may be used to correct one or moredistortions experienced by the external light prior to receipt by theoptical block 160. For example, a correction lens may be located betweenthe front side 120A and the electronic display 155, and configured todistort incoming external light by an amount to counteract an amount ofdistortion experienced by the external light when passing through theelectronic display.

FIG. 1C shows a diagram of the HMD 100 implemented as a near eyedisplay, in accordance with an embodiment. In this embodiment, the HMD100 is in the form of a pair of augmented reality glasses. The HMD 100presents computer-generated media to a user and augments views of aphysical, real-world environment with the computer-generated media.Examples of computer-generated media presented by the HMD 100 includeone or more images, video, audio, or some combination thereof. In someembodiments, audio is presented via an external device (e.g. speakersand headphones) that receives audio information from the HMD 100, aconsole (not shown), or both, and presents audio data based on audioinformation. In some embodiments, the HMD 100 may be modified to alsooperate as a virtual reality (VR) HMD, a mixed reality (MR) HMD, or somecombination thereof. The HMD 100 includes a frame 175 and a display 155.In this embodiment, the frame 175 mounts the near eye display to theuser's head, while the display 155 provides image light to the user. Thedisplay 155 may be customized to a variety of shapes and sizes toconform to different styles of eyeglass frames.

FIG. 1D shows a cross-section view of the HMD 100 implemented as a neareye display. This view includes the frame 175, the display 155 (whichcomprises a display assembly 180 and a display block 185), and the eye170. The display assembly 180 supplies image light to the eye 170. Thedisplay assembly 180 houses the display block 185, which, in differentembodiments, encloses the different types of imaging optics andredirection structures. For purposes of illustration, FIG. 1D shows thecross section associated with a single display block 185 and a singleeye 170, but in alternative embodiments not shown, another display blockwhich is separate from the display block 185 shown in FIG. 1D, providesimage light to another eye of the user.

The display block 185, as illustrated below in FIG. 1D, is configured tocombine light from a local area with light from computer generated imageto form an augmented scene. The display block 185 is also configured toprovide the augmented scene to the eyebox 165 corresponding to alocation of a user's eye 170. The display block 185 may include, e.g., awaveguide display, a focusing assembly, a compensation assembly, or somecombination thereof.

The HMD 100 may include one or more other optical elements between thedisplay block 185 and the eye 150. The optical elements may act to,e.g., correct aberrations in image light emitted from the display block185, magnify image light emitted from the display block 185, some otheroptical adjustment of image light emitted from the display block 185, orsome combination thereof. The example for optical elements may includean aperture, a Fresnel lens, a convex lens, a concave lens, a filter, orany other suitable optical element that affects image light. The displayblock 185 may be composed of one or more materials (e.g., plastic,glass, etc.) with one or more refractive indices that effectivelyminimize the weight and widen a field of view of the HMD 100. In someembodiments, one or more components of the display block 185 areimplemented as a PBP structure having a stack of PBP plates, which aredescribed in greater detail below.

Half-Waveplates

A half-waveplate is a birefringent plane parallel plate, which ischaracterized by its thickness and optic-axis orientation. The thicknessof a half-waveplate is λ/(2Δn) for wavelength λ, where Δn is thebirefringence of the material. The azimuth angle corresponds to theextraordinary principal axis of the birefringent material at a certainpoint.

A half-waveplate introduces a half-wave relative phase differencebetween two eigenpolarizations. Consequently, a half-waveplate mayrotate a linearly polarized incident light to another linearly polarizedexiting light in a different orientation. For example, definingorientation angles in terms of a horizontal axis, if the azimuth angleof a PBP half-waveplate is oriented in a vertical direction (i.e., 90°),linearly polarized incident light having an orientation of 45° may berotated to produce linearly polarized exiting light oriented at −45°. Inanother example, if the azimuth angle of the PBP half-waveplate is22.5°, then the linearly polarized incident light having an orientationof 45° may be rotated to produce linearly polarized exiting lightoriented at 0°.

In addition, a half-waveplate will flip the handedness of circularlypolarized light of the wavelength associated with the half-waveplate,changing right circularly polarized light to left circularly polarizedlight, and vice versa. The absolute phase of the circularly polarizedincident light is shifted depending on the azimuth angle of thehalf-waveplate.

PBP Plates

As discussed above, a PBP structure comprising one or more PBP platesmay be located in an optics block of a HMD or other display device andused to direct or focus light projected by the display. In addition, itis understood that PBP structures described herein may also beimplemented in other optical applications, not just within HMD systems.A PBP plate is a waveplate comprising liquid crystal molecules withspatially varying azimuth angles, and is characterized by its thicknessand the spatial distribution of the azimuth angles. A PBP plate operateson an incident light beam based on the polarization of the beam, whereinthe operation of the PBP plate depends on the spatial distribution ofthe azimuth angles. In some embodiments, a PBP plate may comprise a PBPliquid crystal lens or a PBP liquid crystal grating (also referred to as“PBP lens” and “PBP grating,” respectively).

FIG. 2A is an example PBP liquid crystal lens 200, according to anembodiment. The PBP liquid crystal lens 200 creates a respective lensprofile via an in-plane orientation of the liquid crystal molecule(defined by an azimuth angle Θ), which creates an optical phasedifference T defined as 2Θ. In contrast, a conventional liquid crystallens creates a lens profile via a birefringence (Δn) and layer thickness(d) of liquid crystals, and a number (#) of Fresnel zones (if it isFresnel lens design), in which the phase difference T=Δnd*#*2π/λ.Accordingly, in some embodiments, a PBP liquid crystal lens 200 may havea large aperture size and can be made with a very thin liquid crystallayer, which allows fast switching speed to turn the lens power on/off.

Design specifications for HMDs used for VR, AR, or MR applicationstypically requires a large range of optical power to adapt for human eyevergence-accommodation (e.g., ˜±2 Diopters or more), fast switchingspeeds (e.g., ˜300 ms), and a good quality image. Note conventionalliquid crystal lenses are not well suited to these applications as, aconventional liquid crystal lens generally would require the liquidcrystal to have a relatively high index of refraction or be relativelythick (which reduces switching speeds). In contrast, a PBP liquidcrystal lens is able to meet design specs using a liquid crystal havinga relatively low index of refraction, is thin (e.g., a single liquidcrystal layer can be ˜2 μm), and has high switching speeds (e.g., 300ms).

FIG. 2B is an example of liquid crystal orientations 210 in the PBPliquid crystal lens 200 of FIG. 2A, according to an embodiment. In thePBP liquid crystal lens 200, an azimuth angle (Θ) of a liquid crystalmolecule is continuously changed from a center 220 of the liquid crystallens 200 to an edge 230 of the PBP liquid crystal lens 200, with avaried pitch A. The pitch A indicates a distance in which the azimuthangle of liquid crystal is rotated 180° from the initial state, and maybe a function of the radius of the lens (r). For example, in someembodiments, the azimuth angle Θ of the liquid crystals of the PBP LClens 200 varies based upon distance from the center 220 (radius r), inaccordance with the equation

${{\theta(r)} = \frac{\pi\tau^{2}}{2f_{0}\lambda_{0}}},$where f₀ corresponds to the focal length of the PBP LC lens 200, and λ₀corresponds to wavelength of incident light on the PBP LC lens 200.

FIG. 2C is a section of liquid crystal orientations 240 taken along a yaxis in the PBP liquid crystal lens 200 of FIG. 2A, according to anembodiment. It is apparent from the liquid crystal orientation 240 thata rate of pitch variation is a function of distance from the lens center220. The rate of pitch variation increases with distance from the lenscenter. For example, pitch at the lens center (Λ₀), is the slowest andpitch at the edge 220 (Λ_(r)) is the highest, i.e., Λ₀>Λ₁> . . . >Λ_(r).In the x-y plane, to make a PBP liquid crystal lens with lens radius (r)and lens power (+/−f₀), the azimuth angle needs to meet: 2Θ=r²/f₀*(π/λ₀), where λ₀ is the wavelength of incident light. Along withthe z-axis, a dual twist or multiple twisted structure layers offersachromatic performance on efficiency in the PBP liquid crystal lens 200.Along with the z-axis, the non-twisted structure is simpler to fabricatethen a twisted structure, but is configured for a monochromatic light.

Note that a PBP liquid crystal lens may have a twisted or non-twistedstructure. In some embodiments, a stacked PBP liquid crystal lensstructure may include one or more PBP liquid crystal lenses having atwisted structure, one or more PBP liquid crystal lenses having anon-twisted structure, or some combination thereof.

FIG. 3A is an example PBP liquid crystal grating 300, according to anembodiment. The PBP liquid crystal gratings 300 creates a respectivegrating profile via an in-plane orientation (Θ, azimuth angle) of aliquid crystal molecule, in which the phase difference T=2Θ.

FIG. 3B is an example of liquid crystal orientations 310 in the PBPliquid crystal grating 300 of FIG. 3A, according to an embodiment. Inthe PBP liquid crystal grating 300, an azimuth angle (Θ) of a liquidcrystal molecule is continuously changed along a particular axis (e.g.,the y-axis), with a fixed pitch Λ. For example, as illustrated in FIG.3B, the azimuth angle Θ of the liquid crystal molecules in the PBP LCgrating 300 varies along the y-axis (while being constant along thex-axis), characterized by the equation

${{\theta(y)} = {\frac{\pi\; y}{\Lambda} = {{\pi \cdot y \cdot \sin}\;{\theta/\lambda_{0}}}}},$where θ corresponds to the diffraction angle of the PBP LC grating 300,which is based upon the fixed pitch Λ of the PBP LC grating 300 (e.g.,θ=sin⁻¹(λ₀/Λ)).

FIG. 3C is a section of liquid crystal orientations 340 taken along a yaxis in the PBP liquid crystal grating 300 of FIG. 3A, according to anembodiment. It is apparent from the liquid crystal orientation 340 thata rate of pitch variation is fixed and it is not a function of distancefrom center of grating 320. For example, pitch at the lens center (Λ₀),is the same as pitch at the edges of the grating (Λ_(r)), i.e., Λ₀=Λ₁= .. . =Λ_(r).

In some embodiments, PBP liquid crystal lenses and PBP liquid crystalgratings may be active (also referred to as an active element) orpassive (also referred to as a passive element). An active PBP liquidcrystal lens has three optical states: an additive state, a neutralstate, and a subtractive state. The additive state adds optical power tothe system, the neutral state does not affect the optical power of thesystem (and does not affect the polarization of light passing throughthe active PBP liquid crystal), and the subtractive state subtractsoptical power from the system. The state of an active PBP liquid crystallens is determined by the handedness of polarization of light incidenton the active PBP liquid crystal lens and an applied voltage.

For example, in some embodiments, an active PBP liquid crystal operatesin a subtractive state responsive to incident light with a right handedcircular polarization and an applied voltage of zero (or more generallybelow some minimal value), operates in an additive state responsive toincident light with a left handed circular polarization and the appliedvoltage of zero (or more generally below some minimal value), andoperates in a neutral state (regardless of polarization) responsive toan applied voltage larger than a threshold voltage which aligns liquidcrystal with positive dielectric anisotropy along with the electricfield direction. If the active PBP liquid crystal lens is in theadditive or subtractive state, light output from the active PBP liquidcrystal lens has a handedness opposite that of the light input into theactive PBP liquid crystal lens. In contrast, if the active PBP liquidcrystal lens is in the neutral state, light output from the active PBPliquid crystal lens has the same handedness as the light input into theactive PBP liquid crystal lens.

In contrast, a passive PBP liquid crystal lens has two optical states,specifically, an additive state and a subtractive state. The state of apassive PBP liquid crystal lens is determined by the handedness ofpolarization of light incident on the passive PBP liquid crystal lens. Apassive PBP liquid crystal lens operates in a subtractive stateresponsive to incident light with a right handed polarization andoperates in an additive state responsive to incident light with a lefthanded polarization. The passive PBP liquid crystal lens outputs lightthat has a handedness opposite that of the light input into the passivePBP liquid crystal lens.

An active PBP liquid crystal grating has three optical states (i.e.,additive, subtractive, and neutral), similar to that of an active PBPliquid crystal lens. However, in an additive state, instead of addingoptical power to the system, the additive state causes the active PBPliquid crystal grating to diffract light at a particular wavelength to apositive angle (+θ). Likewise, in the subtractive state, instead ofsubtracting optical power from the system, the subtractive state causesthe active PBP liquid crystal grating to diffract light at theparticular wavelength to a negative angle (−θ). On the other hand, theneutral state does not cause any diffraction of light (and does notaffect the polarization of light passing through the active PBP liquidcrystal grating). The state of an active PBP liquid crystal grating isdetermined by a handedness of polarization of light incident on theactive PBP liquid crystal grating and an applied voltage. An active PBPliquid crystal grating operates in a subtractive state responsive toincident light with a right handed circular polarization and an appliedvoltage of zero (or more generally below some minimal value), operatesin an additive state responsive to incident light with a left handedcircular polarization and the applied voltage of zero (or more generallybelow some minimal value), and operates in a neutral state (regardlessof polarization) responsive to an applied voltage larger than athreshold voltage which aligns liquid crystal with positive dielectricanisotropy along with the electric field direction. If the active PBPliquid crystal grating is in the additive or subtractive state, lightoutput from the active PBP liquid crystal grating has a handednessopposite that of the light input into the active PBP liquid crystalgrating. In contrast, if the active PBP liquid crystal grating is in theneutral state, light output from the active PBP liquid crystal gratinghas the same handedness as the light input into the active PBP liquidcrystal grating.

A PBP plate may be implemented as a half-waveplate characterized by itsthickness and the spatial distribution of it azimuth angles. Forexample, a PBP plate may be a half-waveplate having a thickness ofλ/(2Δn) for a wavelength λ, where Δn is the birefringence of thematerial. As such, the half-wave PBP plate converts a left circularlypolarized incident beam of the wavelength λ into a right circularlypolarized exiting beam with a spatially varying absolute phase.Depending on the spatial distribution of the azimuth angles, theabsolute phase distribution of light exiting the PBP plate varies. Thespatial phase distribution controls the far field distribution of theexiting beam.

In some embodiments, a PBP plate is a PBP grating whose diffractionoperation depends on the incident polarization of an incident beam. Asthe incident beam passes through the plate, the left circularlypolarized part of the beam becomes right circularly polarized anddiffracts in one direction (+1^(st) diffraction order), while the rightcircularly polarized part becomes left circularly polarized anddiffracts in the other direction (−1^(st) diffraction order). Since thePBP plate is designed for a particular wavelength of light (e.g., greenlight), light of other wavelengths (e.g., red and blue light) experiencea less than half-wave or more than half-wave phase shift, causingleakage of the light of other wavelengths in the 0^(th) diffractionorder.

In some embodiments, where the PBP plate is a geometric phase lens, aright circularly incident beam on the PBP lens becomes left circularlypolarized, and converges to a focal plane, forming a real image in theexiting space (˜+1^(st) diffraction order). Similarly, a left circularlyincident beam becomes right circularly polarized, diverges in theexiting space and forms a virtual focal plane in the incident space(˜−1^(st) diffraction order). Since the layer of PBP plate is designedfor a particular wavelength of light (e.g., green light), wavelengths oflight corresponding to other color channels (e.g., red and blue light)will experienced a less than half-wave or more than half-wave phaseshift, causing leakage in the 0^(th) diffraction order.

Color Problem

FIG. 4A illustrates a PBP grating that steers light of different colorchannels at different angles, according to an embodiment. For example,the PBP grating 405 receives incident light comprising light ofdifferent color channels, each color channel associated with a differentwavelength range. Each wavelength range may correspond to a differentportion of a visible band of light (e.g., between 390 and 700 nm). Forexample, the color channels may comprise a red color channel (e.g., maycorrespond to a wavelength of approximately 630 nm), a green colorchannel (e.g., may correspond to a wavelength of approximately 525 nm),and a blue color channel (e.g., may correspond to a wavelength ofapproximately 490 nm). Because the angle at which the PBP grating 405steers incident light is based upon the wavelength of the incidentlight, the light of the different color angles will be steered bydifferent angles.

FIG. 4B illustrates a PBP lens that focuses light of different colorchannels to different focus points, according to an embodiment. Forexample, the PBP lens 410 receives incident light comprising light ofdifferent color channels, each color channel associated with a differentwavelength range (e.g., red, green, and blue color channels). Becausethe focus distance of the PBP lens 410 changes based upon wavelength,the different color channels of incident light do not focus in the samefocal plane.

The thickness of a PBP plate in order to function as half-waveplate iswavelength dependent. In addition, the effect of the periodicity or thedistribution of the azimuth angles of the PBP plate is also wavelengthdependent. As such, incident light of different wavelengths is steeredor focused differently by the PBP plate, causing the incident light toblur or become unfocused.

Half and One-Waveplates

In some embodiments, to achieve achromatic performance, a PBP gratingstructure or lens structure (collectively referred to as a “PBPstructure”) is constructed using a plurality of PBP plates. Each PBPplate of the structure functions as a half-waveplate for a particularcolor channel or wavelength range, and as a one-waveplate for othercolor channels and wavelength ranges. For example, a PBP gratingstructure comprises multiple PBP gratings in order to steer light ofmultiple wavelengths (e.g., three wavelengths, red, green and blue) tothe same angle. Similarly, a PBP lens structure may comprise multiplePBP lenses for steering light of multiple wavelengths to focus in thesame focal plate.

In some embodiments, each of the multiple PBP plates of a PBP structureis associated with a different color channel. For example, inembodiments where the incident light on the PBP structure is dividedinto three color channels (e.g., red, green, and blue), three PBP platesare stacked to achieve apochromatism. Each of the three PBP plates is ahalf-waveplate for a respective wavelength, but a one-waveplate for thewavelengths corresponding to the remaining two PBP plates. Each of therespective wavelengths may correspond to a different color channel(e.g., red, green, and blue). A one-waveplate does not affect thepolarization of the beam, and allows for incident light to pass throughthe waveplate unchanged.

For example, a particular PBP plate may have a thickness correspondingto a single layer half-waveplate for wavelength 525 nm. Assuming thebirefringence Δn is constant through wavelength, the PBP plate functionsas a half-waveplate for light of wavelength 525 nm, and as aone-waveplate for light of wavelength 262.5 nm. Therefore, for incidentlight having a wavelength of 525 nm, the exiting polarization of thelight from the PBP half-waveplate has a spatially varying “absolutephase” when exiting the plate. On the other hand, for light having awavelength of 262.5 nm, the exiting polarization stays the same as theincident polarization, without spatially varying phase change.

In some embodiments, in a PBP grating functioning as a half-waveplatefor wavelength 525 nm (and a one-waveplate for 262.5 nm), the azimuthangles rotate 180 degrees over a spatial distance defined by the pitch Λof the PBP grating. For wavelength 525 nm, the PBP grating diffracts inthe directions following the grating equation (θ_(m)=arcsin(mλ/Λ), wherem is the diffraction order). On the other hand, wavelength 262.5 nmpasses straight through the PBP plate without diffraction.

The far field of exiting beams from the PBP plate can be calculatedthrough Fourier Transform. For example, for the 525 nm beam, the farfield intensity distribution depends on the polarization of the incidentbeam. If the incident beam is perfectly unpolarized, exactly half of theexiting beam (right circularly polarized) diffracts to +1^(st)diffraction direction, and the other half (left circularly polarized)diffracts to −1^(st) diffraction direction. If the incident beam isright circularly polarized, light diffracts as left circularly polarizedlight to the 1^(st) diffraction direction. On the other hand, becausethe PBP plate is a one-waveplate for the 262.5 nm beam, the beam passesthrough the PBP plate un-diffracted.

Apochromatic PBP Grating and Lens Structures

An apochromatic PBP structure (e.g., an apochromatic PBP gratingstructure or an apochromatic PBP lens structure) comprises a series ofPBP plates coupled together, each associated with a different colorchannel. Each PBP plate is configured to function as a half-waveplatefor a particular color channel, and a one waveplate for the remainingcolor channels, and is configured to steer incident light of itsrespective color channel by a common angle or to focus incident light ofits respective color channel to a common focus point. As such, incidentlight of multiple color channels can be steered or focused by the commonangle or to the common focus point.

FIG. 5A illustrates a PBP grating structure 500 composed of a series ofPBP gratings 520, 525, and 530, each configured to operate as a halfwaveplate for a respective color channel, while operating as a onewaveplate (no change) for the other color channels. The PBP gratingstructure receives multi-chromatic incident light 535 comprising a redcolor channel, a green color channel, and a blue color channel. Theincident light 535 propagates through the series of PBP gratings 520,525, and 530, which steers the different color channels of the incidentlight 535 by a common angle θ to form output beams 540, 545, and 550.

For example, the red color channel is diffracted by the PBP grating 520by the angle θ to form the output beam 540, while the green colorchannel is diffracted by the PBP grating 525 by the angle θ to form theoutput beam 545, and the blue color channel is diffracted by the PBPgrating 530 to form the output beam 550. As such, each of the PBPgratings is configured such that light within their respective colorchannel is diffracted to the common angle θ, while having substantiallyno effect on the remaining color channels (e.g., the red color channelpasses through the PBP gratings 525 and 530 substantially unaffected).

FIG. 5B illustrates a PBP lens structure 560 composed of a series of PBPliquid crystal lenses that are each configured to operate as a halfwaveplate for a respective color channel, and operate as a one waveplatefor the remaining color channels. Each of the PBP lenses 580, 585, and590 are configured such that light within their respective color channelis focused to a common point 598.

For example, incident light 595 may comprise a red color channel, greencolor channel, and blue color channel. The red color channel is focusedby the PBP lens 580 towards the common focus point 598. The green colorchannel is focused by the PBP lens 585 towards the common focus point598. The blue color channel is focused by the PBP lens 590 towards thecommon focus point 598.

FIG. 6 illustrates a diagram of an apochromatic PBP grating structure600, in accordance with some embodiments. As illustrated in FIG. 6, thePBP grating structure 600 comprises a first PBP grating 605, a secondPBP grating 610, and a third PBP grating 615, each associated with adifferent color channel (e.g., red, green, and blue). Each of the PBPgratings is a half waveplate for one color corresponding to itsrespective color channel, but a one waveplate for the other two colorscorresponding to the other color channels. As such, each of the PBPgratings 605, 610, and 615 operates as if the waveplate is enabled forone wavelength, but is disabled for other two wavelengths.

Each of the PBP gratings 605, 610, and 615 is configured to steer itsrespective color to a common angle θ. For a given pitch Λ, the angle θat which incident light is steered is wavelength dependent. In order tosteer all three colors to the same angle, the pitch of each of the PBPgratings will be different. For example, the angle θ at which incidentlight is steered can be expressed as a function of wavelength (λ) andpitch (Λ) as follows:

$\begin{matrix}{{\sin\;\theta} = {\frac{\lambda}{\Lambda} = {\frac{\lambda_{Red}}{\Lambda_{Red}} = {\frac{\lambda_{Green}}{\Lambda_{Green}} = \frac{\lambda_{Blue}}{\Lambda_{Blue}}}}}} & (1)\end{matrix}$

Therefore, the pitch Λ_(Red) of the red PBP grating 605 is longer thanthe pitch Λ_(Green) of the green PBP grating 610, which is also longerthan the pitch Λ_(Blue) of the blue PBP grating 615, such that each ofthe gratings is able to steer incident light of its respectivewavelength at the same angle θ. Based upon equation (1) above, the pitchin each grating should follow the equations:

$\begin{matrix}{\Lambda_{Red} = {\Lambda_{Green}*\frac{\lambda_{Red}}{\lambda_{Green}}}} & (2)\end{matrix}$

$\begin{matrix}{\Lambda_{Green} = \frac{\lambda_{Green}}{\sin\;\theta}} & (3)\end{matrix}$

$\begin{matrix}{\Lambda_{Blue} = {\Lambda_{Green}*\frac{\lambda_{Blue}}{\lambda_{Green}}}} & (4)\end{matrix}$

FIG. 7 illustrates another diagram of an apochromatic PBP lens 700, inaccordance with some embodiments. As illustrated in FIG. 7, the PBP lens700 comprises a first PBP lens 705, a second PBP lens 710, and a thirdPBP lens 715. Each of the PBP lens 705, 710, and 715 functions as a halfwaveplate for a particular color channel, but as a one waveplate for theremaining color channels. As such, each PBP lens focuses light of theinput light 720 of the respective color channel to the common focuspoint 725, while being substantially transparent to the portion of theincident light 725 corresponding to the remaining color channels.

Each of the PBP LC lenses 705, 710, and 715 is configured to have aspatially varying LC orientation, wherein the phase or rotation speed ofthe azimuth angle Θ is configured to focus light from the R, G, and Bcolor channels to a common focus (f). In order to bring the focus to thesame focus point, the phase/rotation speed of the azimuth angle Θ_(red)of the red PBP lens 705 is slower than the phase/rotation speed of theazimuth angle Θ_(green) of the green PBP lens 710, which is slower thanthe phase/rotation speed of the azimuth angle Θ_(blue) of the blue PBPlens 715. For example, the focus f of each of the PBP lens 705, 710, and715 may be characterized by:

$\begin{matrix}{{f \approx \frac{\pi r^{2}}{2{\theta\lambda}}} = {\frac{\pi r^{2}}{2\theta_{Red}\lambda_{Red}} = {\frac{\pi r^{2}}{2\theta_{Green}\lambda_{Green}} = \frac{\pi r^{2}}{2\theta_{B\iota ue}\lambda_{B\iota ue}}}}} & (5)\end{matrix}$

Based upon equation (5) above,Θ_(Red)λ_(Red)=Θ_(Green)λ_(Green)=Θ_(Blue)λ_(Blue). As such, the phasein each PBP lens should follow the following equations, where rindicates distance from a center of the PBP lens.

$\begin{matrix}{\theta_{Red} \approx {\theta_{Green}*\frac{\lambda_{Red}}{\lambda_{Green}}}} & (6)\end{matrix}$

$\begin{matrix}{\theta_{Green} \approx {\frac{r^{2}}{2f}*\frac{\pi}{\lambda_{Green}}}} & (7)\end{matrix}$

$\begin{matrix}{\theta_{Blue} \approx {\theta_{Green}*\frac{\lambda_{Blue}}{\lambda_{Green}}}} & (8)\end{matrix}$

In one or more embodiments, a PBP grating structure or a PBP lensstructure includes the following three PBP plates associated with a1^(st) wavelength band, a 2^(nd) wavelength band, and a 3^(rd)wavelength band:

TABLE 1 PBP Plate 1st band 2nd band 3rd band 1^(st) Plate ½ wave 1 wave1 wave 2^(nd) Plate 1 wave ½ wave 1 wave 3^(rd) Plate 1 wave 1 wave ½wave

In some embodiments, the 1^(st), 2^(nd), and 3^(rd) wavelength bandscorrespond to red, green, and blue color channels, respectively. The redcolor channel may correspond to a wavelength of λ_(R)=0.630 μm, whilethe green color channel corresponds to a wavelength of λ_(G)=0.525 μm,and the blue color channel corresponds to a wavelength of λ_(B)=0.490μm.

In some embodiments, it may be difficult to configure a PBP plate tohave a thickness t and material birefringence Δn to provide the exacttarget retardance for all three wavelengths corresponding to the threebands shown above in Table 1. Instead, thicknesses for each of the PBPplates of the PBP structure may be designed to achieve as close to thetarget retardance as possible. The pitches and azimuth angles of eachplate follows the grating equations (Equations (2)-(4) above) or lensequations (Equations (6)-(8) above) for the specific color channelwavelengths.

As discussed above, a PBP plate having a thickness t=λ/(2Δn) functionsas a half-waveplate for light of the wavelength λ. As such, theretardance (birefringence in waves) for a waveplate with thickness t canbe characterized as

${\delta\lbrack{wave}\rbrack} = {\frac{\lambda}{\Delta{nt}}.}$Because retardance cycles through every 360 degrees or every one wave, aone-waveplate, two-waveplate, and three-waveplate (which may be referredto as 0^(th) order, 1^(st) order, and 2^(nd) order one-waveplate,respectively) produce the same net one-wave of retardance. Similarly, ahalf-waveplate, one-and-a-half-waveplate, and two-and-a-half-waveplate(also referred to as 0^(th) order, 1^(st) order, and 2^(nd) orderhalf-waveplate, respectively) all produce a net half-wave of retardance.Therefore, the modulo of the resultant retardance is considered in thecalculation for determining waveplate thickness, providing a certaindegree of freedom in the waveplate design. This modulo of retardance canbe compared to the net ideal retardance as Δδ[waves]=Modulo(δ, 1−idealδ.

In some embodiments, where the “ideal δ” is for the one-wave, the modulois compared to 0 if it is less than 0.5, otherwise the modulo iscompared with 1 if it is larger than 0.5. Similarly, the modulo may becompared to 0.5 for half-wave retardance. The thickness of a PBP platecan found by minimizing a merit function that is the root-mean-square(rms) of the Δδ[waves] for the wavelengths corresponding to each of thecolor channels.

Another degree of freedom of this design is the birefringence Δn of thematerial may vary as function of wavelength. For example, in someembodiments, for a particular PBP plate material, the birefringence forred light may be Δn_(R)=0.2-R, 0.001<R<0.025, while the birefringencefor green light is Δn_(G)=0.2, and the birefringence of blue light isΔn_(B)=0.2+B, 0.001<B<0.025, where R and B correspond to constant valuesbased upon a difference in wavelength between green light and red andblue light, respectively. In some embodiments, R and B correspond toparameters inherent to a type of material used to construct the PBPplates corresponding to the red and blue color channels.

Tables 2, 3, and 4 below illustrate possible designs for PBP plates of aPBP structure configured to receive light from red, green, and bluecolor channels corresponding to the wavelengths described above. The PBPstructure comprises a first PBP plate functioning as a redhalf-waveplate, a second PBP plate functioning as a greenhalf-waveplate, and a third PBP plate functioning as a bluehalf-waveplate. Table 2 shows five possible designs for the first PBPplate functioning as the red half-waveplate (which also functions as agreen one-waveplate and a blue one-waveplate), Table 3 shows fourpossible designs for the second PBP plate functioning as the greenhalf-waveplate (which also functions as a red one-waveplate and a blueone-waveplate), and Table 4 shows four possible designs for the thirdPBP plate functioning the blue half-waveplate (which also functions as ared one-waveplate and a green one-waveplate).

TABLE 2 t μm R B # λ_(R) # λ_(G) # λ_(B) Merit 5.05 0.013 0.001 1.4991.924 2.072 0.0603 5.03 0.010 0.001 1.517 1.916 2.063 0.0614 5.04 0.0120.002 1.501 1.916 2.074 0.0644 5.06 0.017 0.002 1.470 1.928 2.086 0.06725.00 0.007 0.002 1.532 1.905 2.061 0.0679

TABLE 3 t μm R B # λ_(R) # λ_(G) # λ_(B) Merit 6.56 0.008 0.024 1.9992.499 2.999 0.00096 6.57 0.009 0.024 1.992 2.503 3.003 0.0054 14.420.025 0.004 4.006 5.493 6.003 0.0054 6.73 0.016 0.016 1.966 2.564 2.9670.0461

TABLE 4 t μm R B # λ_(R) # λ_(G) # λ_(B) Merit 10.50 0.02 0.01 3 4 4.5 013.13 0.008 0.005 4.002 5.002 5.493 0.004 10.49 0.019 0.01 3.014 3.9964.496 0.009 10.48 0.02 0.011 2.994 3.992 4.513 0.009

As discussed above, the distribution of azimuth angles for each plate iswavelength specific. For example, for a PBP lens, the azimuth angle isin-plane and oriented as Θ=r²/f*(π/λ)/2, where r is the radial distancefrom the center of the lens, and f is the focal length. For a PBPgrating, the pitch Λ indicating revolution of the azimuth determines thesteering angle θ=arcsin(λ/Λ).

Multifocal or Varifocal PBP

In embodiments where a PBP plate is made by active liquid crystal with auniform (non-patterned) conductive layer or liquid crystal monomers, amultifocal image system can be achieved by stacking multiple PBP plateswith electrically switchable half-waveplate in between or in front.

In a case where PBP plate is made by active liquid crystal with finepattern conductive layer, it is possible to use this stack of PBP platesto achieve varying steering angle (in time) for a beam steering PBPplate or varying focal length (in time) for a PBP lens by activelytuning the azimuth angle orientation of each plate.

System Environment

FIG. 8 is a block diagram of one embodiment of a HMD system 800 in whicha console 810 operates. The HMD system 800 may operate in an artificialreality environment. The HMD system 800 shown by FIG. 8 comprises a HMD805 and an input/output (I/O) interface 815 that is coupled to theconsole 810. While FIG. 8 shows an example HMD system 800 including oneHMD 805 and on I/O interface 815, in other embodiments any number ofthese components may be included in the HMD system 800. For example,there may be multiple HMDs 805 each having an associated I/O interface815, with each HMD 805 and I/O interface 815 communicating with theconsole 810. In alternative configurations, different and/or additionalcomponents may be included in the HMD system 800. Additionally,functionality described in conjunction with one or more of thecomponents shown in FIG. 8 may be distributed among the components in adifferent manner than described in conjunction with FIG. 8 in someembodiments. For example, some or all of the functionality of theconsole 810 is provided by the HMD 805.

The HMD 805 is a head-mounted display that presents content to a usercomprising virtual and/or augmented views of a physical, real-worldenvironment with computer-generated elements (e.g., two-dimensional (2D)or three-dimensional (3D) images, 2D or 3D video, sound, etc.). In someembodiments, the presented content includes audio that is presented viaan external device (e.g., speakers and/or headphones) that receivesaudio information from the HMD 805, the console 810, or both, andpresents audio data based on the audio information. The HMD 805 maycomprise one or more rigid bodies, which may be rigidly or non-rigidlycoupled together. A rigid coupling between rigid bodies causes thecoupled rigid bodies to act as a single rigid entity. In contrast, anon-rigid coupling between rigid bodies allows the rigid bodies to moverelative to each other. An embodiment of the HMD 805 is the HMD 100described above in conjunction with FIG. 1A.

The HMD 805 includes a DCA 820, an electronic display 825, an opticalassembly 830, one or more position sensors 835, an IMU 840, an optionaleye tracking system 845, and an optional varifocal module 850. Someembodiments of the HMD 805 have different components than thosedescribed in conjunction with FIG. 8. Additionally, the functionalityprovided by various components described in conjunction with FIG. 8 maybe differently distributed among the components of the HMD 805 in otherembodiments.

The DCA 820 captures data describing depth information of a local areasurrounding some or all of the HMD 805. The DCA 820 can compute thedepth information using the data (e.g., based on a captured portion of astructured light pattern), or the DCA 820 can send this information toanother device such as the console 810 that can determine the depthinformation using the data from the DCA 820.

The electronic display 825 displays two-dimensional or three-dimensionalimages to the user in accordance with data received from the console810. In various embodiments, the electronic display 825 comprises asingle electronic display or multiple electronic displays (e.g., adisplay for each eye of a user). Examples of the electronic display 825include: a liquid crystal display (LCD), an organic light emitting diode(OLED) display, an inorganic light emitting diode (ILED) display, anactive-matrix organic light-emitting diode (AMOLED) display, atransparent organic light emitting diode (TOLED) display, some otherdisplay, or some combination thereof. In some embodiments, theelectronic display 825 may represent the electronic display 155 in FIG.1B.

The optical assembly 830 magnifies image light received from theelectronic display 825, corrects optical errors associated with theimage light, and presents the corrected image light to a user of the HMD805. In some embodiments, the optical assembly 830 corresponds to theoptical block 160 illustrated in FIG. 1B or the display block 185illustrated in FIG. 1D. The optical assembly 830 includes a plurality ofoptical elements, including an apochromatic PBP structure (e.g., a PBPlens structure and/or a PBP grating structure) in accordance with theembodiments described above, configured to adjust incident light fromthe electronic display 825 by a predetermined angle or to focus thelight from the electronic display to a predetermined point. In someembodiments, the optical assembly 830 may further comprises otheroptical elements, such as: an aperture, a Fresnel lens, a convex lens, aconcave lens, a filter, a reflecting surface, or any other suitableoptical element that affects image light. Moreover, the optical assembly830 may include combinations of different optical elements. In someembodiments, one or more of the optical elements in the optical assembly830 may have one or more coatings, such as partially reflective oranti-reflective coatings.

Magnification and focusing of the image light by the optical assembly830 allows the electronic display 825 to be physically smaller, weighless and consume less power than larger displays. Additionally,magnification may increase the field-of-view of the content presented bythe electronic display 825. For example, the field-of-view of thedisplayed content is such that the displayed content is presented usingalmost all (e.g., approximately 110 degrees diagonal), and in some casesall, of the user's field-of-view. Additionally in some embodiments, theamount of magnification may be adjusted by adding or removing opticalelements.

In some embodiments, the optical assembly 830 may be designed to correctone or more types of optical error. Examples of optical error includebarrel or pincushion distortions, longitudinal chromatic aberrations, ortransverse chromatic aberrations. Other types of optical errors mayfurther include spherical aberrations, chromatic aberrations or errorsdue to the lens field curvature, astigmatisms, or any other type ofoptical error. In some embodiments, content provided to the electronicdisplay 825 for display is pre-distorted, and the optical assembly 830corrects the distortion when it receives image light from the electronicdisplay 825 generated based on the content. In some embodiments, theoptical assembly 830 comprises a pancake lens assembly and an absorptivelinear polarizer to mitigate the Narcissus effect without affectingimage brightness. In some embodiments, the optical assembly 830 furthercomprises a waveplate, such as a PBP structure (e.g., a PBP gratingstructure or a PBP lens structure as described above). In someembodiments, the optical assembly 830 may represent the optical block160 illustrated in FIG. 1B or the display block 185 illustrated in FIG.1D.

The IMU 840 is an electronic device that generates data indicating aposition of the HMD 805 based on measurement signals received from oneor more of the position sensors 835 and from depth information receivedfrom the DCA 820. A position sensor 835 generates one or moremeasurement signals in response to motion of the HMD 805. Examples ofposition sensors 835 include: one or more accelerometers, one or moregyroscopes, one or more magnetometers, another suitable type of sensorthat detects motion, a type of sensor used for error correction of theIMU 840, or some combination thereof. The position sensors 835 may belocated external to the IMU 840, internal to the IMU 840, or somecombination thereof.

Based on the one or more measurement signals from one or more positionsensors 835, the IMU 840 generates data indicating an estimated currentposition of the HMD 805 relative to an initial position of the HMD 805.For example, the position sensors 835 include multiple accelerometers tomeasure translational motion (forward/back, up/down, left/right) andmultiple gyroscopes to measure rotational motion (e.g., pitch, yaw,roll). In some embodiments, the position sensors 835 may represent theposition sensors 140 in FIG. 1A. In some embodiments, the IMU 840rapidly samples the measurement signals and calculates the estimatedcurrent position of the HMD 805 from the sampled data. For example, theIMU 840 integrates the measurement signals received from theaccelerometers over time to estimate a velocity vector and integratesthe velocity vector over time to determine an estimated current positionof a reference point on the HMD 805. Alternatively, the IMU 840 providesthe sampled measurement signals to the console 810, which interprets thedata to reduce error. The reference point is a point that may be used todescribe the position of the HMD 805. The reference point may generallybe defined as a point in space or a position related to the HMD's 805orientation and position.

The IMU 840 receives one or more parameters from the console 810. Theone or more parameters are used to maintain tracking of the HMD 805.Based on a received parameter, the IMU 840 may adjust one or more IMUparameters (e.g., sample rate). In some embodiments, certain parameterscause the IMU 840 to update an initial position of the reference pointso it corresponds to a next position of the reference point. Updatingthe initial position of the reference point as the next calibratedposition of the reference point helps reduce accumulated errorassociated with the current position estimated the IMU 840. Theaccumulated error, also referred to as drift error, causes the estimatedposition of the reference point to “drift” away from the actual positionof the reference point over time. In some embodiments of the HMD 805,the IMU 840 may be a dedicated hardware component. In other embodiments,the IMU 840 may be a software component implemented in one or moreprocessors. In some embodiments, the IMU 840 may represent the IMU 130in FIG. 1A.

In some embodiments, the eye tracking system 845 is integrated into theHMD 805. The eye tracking system 845 determines eye tracking informationassociated with an eye of a user wearing the HMD 805. The eye trackinginformation determined by the eye tracking system 845 may compriseinformation about an orientation of the user's eye, i.e., informationabout an angle of an eye-gaze. In some embodiments, the eye trackingsystem 845 is integrated into the optical assembly 830. An embodiment ofthe eye-tracking system 845 may comprise an illumination source and animaging device (camera).

In some embodiments, the varifocal module 850 is further integrated intothe HMD 805. The varifocal module 850 may be coupled to the eye trackingsystem 845 to obtain eye tracking information determined by the eyetracking system 845. The varifocal module 850 may be configured toadjust focus of one or more images displayed on the electronic display825, based on the determined eye tracking information obtained from theeye tracking system 845. In this way, the varifocal module 850 canmitigate vergence-accommodation conflict in relation to image light. Thevarifocal module 850 can be interfaced (e.g., either mechanically orelectrically) with at least one of the electronic display 825 and atleast one optical element of the optical assembly 830. Then, thevarifocal module 850 may be configured to adjust focus of the one ormore images displayed on the electronic display 825 by adjustingposition of at least one of the electronic display 825 and the at leastone optical element of the optical assembly 830, based on the determinedeye tracking information obtained from the eye tracking system 845. Byadjusting the position, the varifocal module 850 varies focus of imagelight output from the electronic display 825 towards the user's eye. Thevarifocal module 850 may be also configured to adjust resolution of theimages displayed on the electronic display 825 by performing foveatedrendering of the displayed images, based at least in part on thedetermined eye tracking information obtained from the eye trackingsystem 845. In this case, the varifocal module 850 provides appropriateimage signals to the electronic display 825. The varifocal module 850provides image signals with a maximum pixel density for the electronicdisplay 825 only in a foveal region of the user's eye-gaze, whileproviding image signals with lower pixel densities in other regions ofthe electronic display 825. In one embodiment, the varifocal module 850may utilize the depth information obtained by the DCA 820 to, e.g.,generate content for presentation on the electronic display 825.

The I/O interface 815 is a device that allows a user to send actionrequests and receive responses from the console 810. An action requestis a request to perform a particular action. For example, an actionrequest may be an instruction to start or end capture of image or videodata or an instruction to perform a particular action within anapplication. The I/O interface 815 may include one or more inputdevices. Example input devices include: a keyboard, a mouse, a gamecontroller, or any other suitable device for receiving action requestsand communicating the action requests to the console 810. An actionrequest received by the I/O interface 815 is communicated to the console810, which performs an action corresponding to the action request. Insome embodiments, the I/O interface 815 includes an IMU 840 thatcaptures calibration data indicating an estimated position of the I/Ointerface 815 relative to an initial position of the I/O interface 815.In some embodiments, the I/O interface 815 may provide haptic feedbackto the user in accordance with instructions received from the console810. For example, haptic feedback is provided when an action request isreceived, or the console 810 communicates instructions to the I/Ointerface 815 causing the I/O interface 815 to generate haptic feedbackwhen the console 810 performs an action.

The console 810 provides content to the HMD 805 for processing inaccordance with information received from one or more of: the DCA 820,the HMD 805, and the I/O interface 815. In the example shown in FIG. 8,the console 810 includes an application store 855, a tracking module860, and an engine 865. Some embodiments of the console 810 havedifferent modules or components than those described in conjunction withFIG. 8. Similarly, the functions further described below may bedistributed among components of the console 810 in a different mannerthan described in conjunction with FIG. 8.

The application store 855 stores one or more applications for executionby the console 810. An application is a group of instructions, that whenexecuted by a processor, generates content for presentation to the user.Content generated by an application may be in response to inputsreceived from the user via movement of the HMD 805 or the I/O interface815. Examples of applications include: gaming applications, conferencingapplications, video playback applications, or other suitableapplications.

The tracking module 860 calibrates the HMD system 800 using one or morecalibration parameters and may adjust one or more calibration parametersto reduce error in determination of the position of the HMD 805 or ofthe I/O interface 815. For example, the tracking module 860 communicatesa calibration parameter to the DCA 820 to adjust the focus of the DCA820 to more accurately determine positions of structured light elementscaptured by the DCA 820. Calibration performed by the tracking module860 also accounts for information received from the IMU 840 in the HMD805 and/or an IMU 840 included in the I/O interface 815. Additionally,if tracking of the HMD 805 is lost (e.g., the DCA 820 loses line ofsight of at least a threshold number of structured light elements), thetracking module 860 may re-calibrate some or all of the HMD system 800.

The tracking module 860 tracks movements of the HMD 805 or of the I/Ointerface 815 using information from the DCA 820, the one or moreposition sensors 835, the IMU 840 or some combination thereof. Forexample, the tracking module 850 determines a position of a referencepoint of the HMD 805 in a mapping of a local area based on informationfrom the HMD 805. The tracking module 860 may also determine positionsof the reference point of the HMD 805 or a reference point of the I/Ointerface 815 using data indicating a position of the HMD 805 from theIMU 840 or using data indicating a position of the I/O interface 815from an IMU 840 included in the I/O interface 815, respectively.Additionally, in some embodiments, the tracking module 860 may useportions of data indicating a position or the HMD 805 from the IMU 840as well as representations of the local area from the DCA 820 to predicta future location of the HMD 805. The tracking module 860 provides theestimated or predicted future position of the HMD 805 or the I/Ointerface 815 to the engine 855.

The engine 865 generates a 3D mapping of the area surrounding some orall of the HMD 805 (i.e., the “local area”) based on informationreceived from the HMD 805. In some embodiments, the engine 865determines depth information for the 3D mapping of the local area basedon information received from the DCA 820 that is relevant for techniquesused in computing depth. The engine 865 may calculate depth informationusing one or more techniques in computing depth from structured light.In various embodiments, the engine 865 uses the depth information to,e.g., update a model of the local area, and generate content based inpart on the updated model.

The engine 865 also executes applications within the HMD system 800 andreceives position information, acceleration information, velocityinformation, predicted future positions, or some combination thereof, ofthe HMD 805 from the tracking module 860. Based on the receivedinformation, the engine 865 determines content to provide to the HMD 805for presentation to the user. For example, if the received informationindicates that the user has looked to the left, the engine 865 generatescontent for the HMD 805 that mirrors the user's movement in a virtualenvironment or in an environment augmenting the local area withadditional content. Additionally, the engine 865 performs an actionwithin an application executing on the console 810 in response to anaction request received from the I/O interface 815 and provides feedbackto the user that the action was performed. The provided feedback may bevisual or audible feedback via the HMD 805 or haptic feedback via theI/O interface 815.

In some embodiments, based on the eye tracking information (e.g.,orientation of the user's eye) received from the eye tracking system845, the engine 865 determines resolution of the content provided to theHMD 805 for presentation to the user on the electronic display 825. Theengine 865 provides the content to the HMD 805 having a maximum pixelresolution on the electronic display 825 in a foveal region of theuser's gaze, whereas the engine 865 provides a lower pixel resolution inother regions of the electronic display 825, thus achieving less powerconsumption at the HMD 805 and saving computing cycles of the console810 without compromising a visual experience of the user. In someembodiments, the engine 865 can further use the eye tracking informationto adjust where objects are displayed on the electronic display 825 toprevent vergence-accommodation conflict.

Additional Configuration Information

The foregoing description of the embodiments has been presented for thepurpose of illustration; it is not intended to be exhaustive or to limitthe patent rights to the precise forms disclosed. Persons skilled in therelevant art can appreciate that many modifications and variations arepossible in light of the above disclosure.

Any of the steps, operations, or processes described herein may beperformed or implemented with one or more hardware or software modules,alone or in combination with other devices. In one embodiment, asoftware module is implemented with a computer program productcomprising a computer-readable medium containing computer program code,which can be executed by a computer processor for performing any or allof the steps, operations, or processes described.

Embodiments of the disclosure may also relate to an apparatus forperforming the operations herein. This apparatus may be speciallyconstructed for the required purposes, and/or it may comprise ageneral-purpose computing device selectively activated or reconfiguredby a computer program stored in the computer. Such a computer programmay be stored in a non-transitory, tangible computer readable storagemedium, or any type of media suitable for storing electronicinstructions, which may be coupled to a computer system bus.Furthermore, any computing systems referred to in the specification mayinclude a single processor or may be architectures employing multipleprocessor designs for increased computing capability.

Embodiments of the disclosure may also relate to a product that isproduced by a computing process described herein. Such a product maycomprise information resulting from a computing process, where theinformation is stored on a non-transitory, tangible computer readablestorage medium and may include any embodiment of a computer programproduct or other data combination described herein.

The language used in the specification has been principally selected forreadability and instructional purposes, and it may not have beenselected to delineate or circumscribe the inventive subject matter. Itis therefore intended that the scope of the patent rights be limited notby this detailed description, but rather by any claims that issue on anapplication based hereon. Accordingly, the disclosure of the embodimentsis intended to be illustrative, but not limiting, of the scope of thepatent rights, which is set forth in the following claims.

What is claimed is:
 1. A liquid crystal structure comprising: a firstliquid crystal element having a first thickness selected to change apolarization and adjust light of a first wavelength range correspondingto a first color channel by a first amount, and to maintain apolarization of light of a second wavelength range different from thefirst wavelength range corresponding to a second color channel; and asecond liquid crystal element configured to receive light through thefirst liquid crystal element, and having a second thickness selected tochange a polarization of and adjust light of the second wavelength rangeby the first amount, and to maintain a polarization of light of thefirst wavelength range.
 2. The liquid crystal structure of claim 1,wherein the first liquid crystal element is a first liquid crystalgrating configured to adjust light of the first wavelength range to afirst angle, and the second liquid crystal element is a second liquidcrystal grating configured to adjust light of the second wavelengthrange to the first angle.
 3. The liquid crystal structure of claim 2,wherein the first liquid crystal grating has a first pitch, and thesecond liquid crystal grating has a second pitch that is different thanthe first pitch.
 4. The liquid crystal structure of claim 3, wherein thefirst and second liquid crystal gratings are configured such that aratio of the first pitch to the second pitch matches a ratio between awavelength of the first wavelength range and a wavelength of the secondwavelength range.
 5. The liquid crystal structure of claim 1, whereinthe first liquid crystal element is a first liquid crystal lensconfigured to focus light of the first wavelength range to a firstlocation, and the second liquid crystal element is a second liquidcrystal lens configured to focus light of the second wavelength range tothe first location.
 6. The liquid crystal structure of claim 5, whereinthe first liquid crystal lens has a first liquid crystal rotation speed,and the second liquid crystal lens has a second liquid crystal rotationspeed that is different than the first liquid crystal rotation speed. 7.The liquid crystal structure of claim 6, wherein a ratio of the firstrotation speed to the second rotation speed matches a ratio between awavelength of the first wavelength range and a wavelength of the secondwavelength range.
 8. The liquid crystal structure of claim 1, whereinthe first and second liquid crystal elements are stacked to form astacked structure configured to receive light comprising at least lightof the first wavelength range and light of the second wavelength range,the light passing through the first and second liquid crystal elementsin sequence.
 9. The liquid crystal structure of claim 1, wherein thefirst thickness is selected to minimize an aggregation of: a firstdifference between 0.5 and a first modulo between a first wavelength ofthe first wavelength range and a product of the first thickness and abirefringence of a material of the first liquid crystal element forlight of the first wavelength, and a second difference between 0 or 1and a second modulo between a second wavelength of the second wavelengthrange and a product of the first thickness and a birefringence of thematerial for light of the second wavelength.
 10. The liquid crystalstructure of claim 1, further comprising: a third liquid crystal elementhaving a third thickness selected to change a polarization and adjustlight of a third wavelength range corresponding to a third color channelby the first amount, and to maintain a polarization of light of thefirst and second wavelength ranges, and wherein the first thickness ofthe first liquid crystal element and the second thickness of the secondliquid crystal element are further selected to maintain a polarizationlight of the third wavelength range.
 11. The liquid crystal structure ofclaim 1, wherein the first and second liquid crystal elements are partof an optical assembly of a head-mounted display (HMD).
 12. Ahead-mounted display (HMD), comprising: an electronic display configuredto emit image light that is inclusive of a set of color channels, eachcorresponding to a respective wavelength range; an optical assemblyconfigured to adjust the image light using a liquid crystal structure,the liquid crystal structure comprising: a first liquid crystal elementhaving a first thickness selected to change a polarization and adjustlight of a first wavelength range corresponding to a first color channelof the set of color channels by a first amount, and to maintain apolarization of light of a second wavelength range corresponding to asecond color channel of the set of color channels; and a second liquidcrystal element configured to receive light through the first liquidcrystal element, and having a second thickness selected to change apolarization of and adjust light of the second wavelength range by thefirst amount, and to maintain a polarization of light of the firstwavelength range.
 13. The HMD of claim 12, wherein the first liquidcrystal element is a first liquid crystal grating configured to adjustlight of the first wavelength range to a first angle, and the secondliquid crystal element is a second liquid crystal grating configured toadjust light of the second wavelength range to the first angle.
 14. TheHMD of claim 13, wherein the first liquid crystal grating has a firstpitch, and the second liquid crystal grating has a second pitch that isdifferent than the first pitch.
 15. The HMD of claim 14, wherein thefirst and second liquid crystal gratings are configured such that aratio of the first pitch to the second pitch matches a ratio between awavelength of the first wavelength range and a wavelength of the secondwavelength range.
 16. The HMD of claim 12, wherein the first liquidcrystal element is a first liquid crystal lens configured to focus lightof the first wavelength range to a first location, and the second liquidcrystal element is a second liquid crystal lens configured to focuslight of the second wavelength range to the first location.
 17. The HMDof claim 16, wherein the first liquid crystal lens has a first liquidcrystal rotation speed, and the second liquid crystal lens has a secondliquid crystal rotation speed that is different than the first liquidcrystal rotation speed, and wherein a ratio of the first rotation speedto the second rotation speed matches a ratio between a wavelength of thefirst wavelength range and a wavelength of the second wavelength range.18. The HMD of claim 12, wherein the first and second liquid crystalelements are stacked to form a stacked structure configured to receive alight comprising at least light of the first wavelength range and lightof the second wavelength range, the light passing through the first andsecond liquid crystal elements in sequence.
 19. The HMD of claim 12,wherein the first thickness is selected to minimize an aggregation of: afirst difference between 0.5 and a first modulo between a firstwavelength of the first wavelength range and a product of the firstthickness and a birefringence of a material of the first liquid crystalelement for light of the first wavelength, and a second differencebetween 0 or 1 and a second modulo between a second wavelength of thesecond wavelength range and a product of the first thickness and abirefringence of the material for light of the second wavelength. 20.The HMD of claim 12, wherein the liquid crystal structure furthercomprises: a third liquid crystal element having a third thicknessselected to change a polarization and adjust light of a third wavelengthrange corresponding to a third color channel by the first amount, and tomaintain a polarization of light of the first and second wavelengthranges, and wherein the first thickness of the first liquid crystalelement and the second thickness of the second liquid crystal elementare further selected to maintain a polarization light of the thirdwavelength range.